> if there was some specific target they could throw a lot of computing resources at it

1. Yes, for many (too many) values of they. "Your" government, all governments, so essentially any corporation, or any private individual that can afford time or computing resources and is interested in a target.

2. This scheme doesn't age well. Targets' mandatory low-grade encrypted communications today could be saved as blackmail time capsules, much more easily decrypted with cheap resources in the too-near future.